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Positivity and matrix inequalities: some reminiscences of K. R. Parthasarathy
One of K. R. Parthasarathy’s major and abiding interests was the theory of positive definite functions and especially its relation to classical and...
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On a supercritical k-Hessian inequality of Trudinger–Moser type and extremal functions
We establish a supercritical Trudinger–Moser type inequality for the k -Hessian operator on the space of the k -admissible radially symmetric functions
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Khasminskii’s Theorem for the Kolmogorov Equation with Partially Degenerate Diffusion Matrix
AbstractThe stationary Kolmogorov equation with partially degenerate diffusion matrix and discontinuous drift coefficient is studied. Sufficient...
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On the Probability of Generating a Primitive Matrix
Given a k × n integer primitive matrix
A (i.e., a matrix can be extended to an n × n unimodular matrix over the integers) with the maximal absolute... -
A New Carleman Inequality for a Linear Schrödinger Equation on Some Unbounded Domains
This article presents a new Carleman inequality for a linear Schrödinger equation which is suitable for both bounded and unbounded domains. We...
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Pseudo-Differential Operators on Matrix Weighted Besov–Triebel–Lizorkin Spaces
We characterize the matrix-weighted Triebel–Lizorkin spaces and Besov spaces by Peetre maximal function and approximation. Using these...
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A modified inertial Tseng technique of Bilevel variational inequality problem with application to image processing
In this paper, we propose and study a new modified Tseng inertial iterative technique for solving Bilevel quasimonotone Variational Inequality...
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A Penrose-Type Inequality with Angular Momenta for Black Holes with 3-Sphere Horizon Topology
We establish a Penrose-type inequality with angular momentum for four-dimensional, biaxially symmetric, maximal, asymptotically flat initial...
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Ando-Hiai Inequality: Extensions and Applications
The Ando-Hiai inequality says that if A# α B ≤ I for a fixed α ∈ [0, 1] and positive invertible operators A, B on a Hilbert space, then...
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The Case of Equality in Geometric Instances of Barthe’s Reverse Brascamp-Lieb Inequality
The works of Bennett, Carbery, Christ, Tao and of Valdimarsson have clarified when equality holds in the Brascamp-Lieb inequality. Here we...
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On the convergence of numerical integration as a finite matrix approximation to multiplication operator
We study the convergence of a family of numerical integration methods where the numerical integration is formulated as a finite matrix approximation...
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Length Function and Simultaneous Triangularization of Matrix Pairs
The paper interrelates the simultaneous triangularization problem for matrix pairs with the Paz problem and known results on the length of the matrix...
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Nonlinear matrix equations involving Kubo–Ando means
In this paper, we consider two generalized matrix equations that involve an arbitrary Kubo–Ando mean. We also study the multi-step stationary...
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Aubin Type Almost sharp Moser–Trudinger Inequality Revisited
We give a new proof of the almost sharp Moser–Trudinger inequality on smooth compact Riemannian manifolds based on the sharp Moser inequality on...
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Convergence Analysis of a New Bregman Extragradient Method for Solving Fixed Point Problems and Variational Inequality Problems in Reflexive Banach Spaces
We mainly introduce a new self-adaptive extragradient method by using the inertial technique for solving variational inequality problems of...
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Freedman Inequality in Noncommutative Probability Spaces
The classical Freedman inequality, as a martingale extension of the Bernstein inequality, gives an upper bound for the tail probabilities of a...
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A New Halpern-Type Bregman Projection Method for Solving Variational Inequality Problems in Reflexive Banach Space
This paper proposes a new Halpern-type inertial subgradient extragradient method with Bregman distance for solving variational inequality problems in...
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Levitin–Polyak Well-Posedness by Perturbations for the Split Hemivariational Inequality Problem on Hadamard Manifolds
The purpose of this paper is to establish some new results on the Levitin–Polyak well-posedness to a class of split hemivariational inequality...